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Numerical analysis in digital signal processingColloquium
|Speaker: ||Professor Thomas Strohmer, Mathematics, UC Davis|
|Location: ||693 Kerr|
|Start time: ||Mon, Oct 4 1999, 4:10PM|
In my talk I will consider two topics that play an important role in digital
signal processing: (i) Signal reconstruction and (ii) Time-Frequency
analysis based on Weyl-Heisenberg systems.
In the first part of my talk I give an overview of recent developments
in the problem of reconstructing a band-limited signal from non-uniform
s ampling from a numerical analysis view point. Among others it is shown
how the choice of the finite-dimensional model determines the efficiency
and robustness of the resulting numerical al gorithms.In the one approach
(often proposed in the literature) the finite-dimensional model leads
to an ill-posed problem even in very simple situations. The
other model that we consider leads to a well-posed problem that preserves
important structural properties of the original infinite-dimensional
problem and gives rise to efficient numerical algorithms.
In the second part of the talk I will focus on Weyl-Heisenberg (Gabor)
systems. A Weyl-Heisenberg system is generated from a single function by
translations and modulations. These systems play for instance a crucial
role in modern communication systems. I will address some some numerical
aspects of Weyl-Heisenberg systems.